Pseudorandom function family

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Definitions:

An indexed family of (efficiently computable) functions, each defined for the same particular pair of input and output spaces. (For the purposes of this Recommendation, one may assume that both the index set and the output space are finite.) The indexed functions are pseudorandom in the following sense:

If a function from the family is selected by choosing an index value uniformly at random, and one’s knowledge of the selected function is limited to the output values corresponding to a feasible number of (adaptively) chosen input values, then the selected function is computationally indistinguishable from a function whose outputs were fixed uniformly at random.

Sources:
NIST SP 800-56C Rev. 2

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